1. CSC 110 – Fluency in Information Technology Chapter 20: The random function and Chaos
Dr. Curry Guinn

2. Today’s Class
Random Number Generation
Randomness and Chaos Theory

3. Math.random()
A common operation we want to perform with computers is to generate a random number
We use this for
Games (random shuffle, random throw of dice)
Running simulations
Having our programs (like games) behave in ways we haven’t seen before
HiLo.java

4. How can a deterministic machine generate a random number?
Remember: Computers are deterministic
Given the same instructions, they perform the same thing every time
So what’s random?
Random numbers are generated using a pseudo-random number generator (PNG).
The numbers aren’t really random but the sequence is so complex, humans can’t see the patterns.
random_seed = random_seed * ;
random_number = (random_seed / 65536) % 32768
Random.htm

5. Seeding a pseudo-random number generator
The PNGs that computers use will generate the exact same “random” series of numbers given the same initial input (called the seed)
Some common seeds that computers use
Number of seconds since 1900
Number of milliseconds since the machine was booted
Scientist often control the seed so they can run exactly the same “random” experiment again

6. Case Study: Online Poker Room
The Link:
The Setting
1999
PlanetPoker internet card room
Texas Hold’Em
PlanetPoker published their random shuffling algorithm to demonstrate their integrity
Common practice among internet card rooms

7. How many possible shuffles in Poker?
There are 52 cards so …
52 possibilities for the top card
51 possibilities for the 2nd card
50 possibilities for the 3rd card …
52*51*50*…*2*1 = 52!
2^ … a really, really big number
Approximately 10^68

8. PlanetPoker’s PNG
Randomize() uses the number of milliseconds since midnight
There are only 86,400,000 milliseconds in a day
Therefore, they can only generate 86,400,000 possible shuffles (much less than 10^68)
Further, by synchronizing with their clock, you can get very close to guessing their time

9. Texas Hold’Em
In Texas Hold’Em, each player gets two down cards and then all the players will share five up cards
After an initial round of betting, where the players only see their hole cards, the first 3 shared cards are turned face up (called the flop)

10. At the time of the flop
At the flop, a player knows a sequence of 5 cards in the shuffle.
What is the likelihood of seeing those 5 cards in a shuffle? 52*51*50*49*48
1 in 311,875,200
These odds are such that we can find the “random” shuffle out of the set of 86,000,000 possible decks
Once we find it, we know the all the cards dealt (and to be dealt)
(Further, we also know what seed they used for that shuffle making it easier to synchronize our clocks)

11. What Poker Rooms Do Now Seed is modified by PokerStars
User input: mouse movements, timing events
True hardware random number generators (Intel’s for instance uses thermal “noise”)
Other hardware solutions: quantum mechanics
PokerStars

12. What is Chaos Theory?
Traditional notion of chaos – unorganized, disorderly, random etc.
But Chaos Theory has little to do with that traditional notion
On the contrary, it actually tells you that not all that ‘chaos’ you see is due to chance, or random or caused by unknown factors
Oxymoron term coined “Deterministic Randomness”
Chaos Theory – It’s about the deterministic factors (non-linear relationships) that cause things to look random

13. A Simple Equation
Xt = Xt-12 + c
Chaos.zip
If c = -1.1

17. C = -1.9

18. Chaotic Systems are Extremely Vulnerable to Initial Conditions
The Butterfly Effect

20. Initial Conditions X(t0), Y(t0), Z(t0)...
Clockwork Universe
determimistic non-chaotic
Initial Conditions X(t0), Y(t0), Z(t0)...
Can
compute
all future
X(t), Y(t), Z(t)...
Equations

21. Initial Conditions X(t0), Y(t0), Z(t0)...
Chaotic Universe
determimistic chaotic
Initial Conditions X(t0), Y(t0), Z(t0)...
sensitivity
to initial
conditions
Can not
compute
all future
X(t), Y(t), Z(t)...
Equations

22. Why Should You Care?
Any complex process is vulnerable to chaotic behavior
Weather
Financial systems
Economic theory
Stock market
Population models
Physics
Biology
Chemistry